theories:classical_mechanics
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theories:classical_mechanics [2018/05/04 09:44] jakobadmin [Formulations] |
theories:classical_mechanics [2023/05/20 03:16] (current) 50.24.47.35 [Formulations] |
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| <tabbox Formulations> | <tabbox Formulations> | ||
| + | There are different ways of describing classical mechanics. Each has its individual strength and weaknesses, but in terms of observable predictions, they are all equivalent. | ||
| - | + | * [[theories:classical_mechanics:newtonian]] $\leftrightarrow$ classical mechanics in real space | |
| - | * [[theories:classical_mechanics:newtonian_mechanics]] $\leftrightarrow$ classical mechanics in real space: Euclidean $\mathbb{R}^3$ or Minkowski space $\mathbb{R}^{(3,1)}$. | + | * [[theories:classical_mechanics:lagrangian]] $\leftrightarrow$ classical mechanics in [[basic_tools:configuration_space|configuration space]] |
| + | * [[theories:classical_mechanics:hamiltonian]] $\leftrightarrow$ classical mechanics in [[basic_tools:phase_space|phase space]] | ||
| * [[theories:classical_mechanics:koopman_von_neumann_mechanics]] $\leftrightarrow$ classical mechanics in [[basic_tools:hilbert_space|Hilbert space]] | * [[theories:classical_mechanics:koopman_von_neumann_mechanics]] $\leftrightarrow$ classical mechanics in [[basic_tools:hilbert_space|Hilbert space]] | ||
| - | * [[theories:classical_mechanics:hamiltonian_mechanics]] $\leftrightarrow$ classical mechanics in [[basic_tools:phase_space|phase space]] | + | |
| - | * [[theories:classical_mechanics:lagrangian_mechanics]] $\leftrightarrow$ classical mechanics in [[basic_tools:configuration_space|configuration space]] | + | <tabbox Roadmaps> |
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| + | **Traditional Roadmap** | ||
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| + | <diagram> | ||
| + | | AA|~@2| Newton's laws |AA=[[theories:classical_mechanics:newtonian]] | ||
| + | | |!@4| | | | | | | ||
| + | | AA|~@2| Euler-Lagrange equation, Noether's theorem, configuration space |AA=[[theories:classical_mechanics:lagrangian]] | ||
| + | | |!@4| | | | | | | ||
| + | | AA|~@2| Hamilton's equation, canonical transformation, generating functions, Noether's theorem in the Hamiltonian formalism, phase space |AA=[[theories:classical_mechanics:hamiltonian]] | ||
| + | </diagram> | ||
| + | |||
| + | ---- | ||
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| + | **Reading Recommendations** | ||
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| + | * The best book that gives a grand tour of classical mechanics is The Lazy Universe by Coopersmith | ||
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| + | <tabbox History> | ||
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| + | * A History of Mechanics by Dugas | ||
| </tabbox> | </tabbox> | ||
theories/classical_mechanics.1525419878.txt.gz · Last modified: 2018/05/04 07:44 (external edit)
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